Mortgage Math

Mortgage Math.carbide.md

Mortgage Math

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amortization.js

function Amortization(InitialBalance,R,T,Output){
    var Interest       = []; 
	var Principal      = []; 
	var Balance        = [InitialBalance]; 
    var A              = (1/R) * (1 - 1/((1+R)**T));
    var Pmt = InitialBalance/A;
	for(var t = 1; t <= T; t++){
    	Interest.push(Balance[t-1]*R)
    	Principal.push(Pmt - Balance[t-1]*R)
    	Balance.push(Balance[t-1] - Principal[t-1])
	}
	if (Output == 'InterestPayment')  { return Interest  }
    if (Output == 'PrincipalPayment') { return Principal } 
    if (Output == 'RemainingBalance') { return Balance   }
}






/// ################################
/// ################################

var InitialBalance = 500; ///++InitialBalance:++ **Amount you borrow** from the bank (in $1000s).
var R = 0.06 / 12; ///++R:++ Monthly **mortgage rate**.
var T = 30 * 12; ///++T:++ **How long** it takes **until you to pay off principal** you owe if you keep on making the **same monthly payments**? a.k.a., amortization period.

/// ################################
/// ################################

var A = (1/R) * (1 - 1/((1+R)**T)); ///++A:++ **Present value** of a **T-month $1 annuity** if the **monthly interest rate is R**.
var MonthlyPayment = InitialBalance / A; ///++MonthlyPayment:++ **Amount you pay** each month (in $1000s) for **next T months** if you **borrow InitialBalance** from the bank when the monthly **mortgage rate is R**.

/// ################################
///################################

var RemainingBalance = Amortization(InitialBalance,R,T,'RemainingBalance'); ///++RemainingBalance:++ **Amount of money** (in $1000s) that **you still owe** the bank **after month t payment**. Note that InitialBalance = RemainingBalance in month t=0.
var InterestPayment  = Amortization(InitialBalance,R,T,'InterestPayment'); ///++InterestPayment:++ **Part of payment** in month t (in $1000s) **that does not affect remaining balance**.
var PrincipalPayment = Amortization(InitialBalance,R,T,'PrincipalPayment'); ///++PrincipalPayment:++ **Part of payment** in month t (in $1000s) that goes towards** lowering your remaining balance**.

annuityFormula.js

function AnnuityPayments(T){
    var AnnuityPayments = [];
	for(var t = 1; t <= T; t++){ 
    	AnnuityPayments.push(1) 
	}
    return AnnuityPayments
}

function PresentValue(Payments,R){
    var PaymentsPV = [];
	for(var t = 1; t <= T; t++){ 
    	PaymentsPV.push(Payments[t-1]/(1+R)**t) 
	}
    return PaymentsPV
}
function Sum(PaymentsPV){
    var SumOfPaymentsPV = 0;
    var T = PaymentsPV.length;
	for(var t = 0; t < T; t++) { 
    	SumOfPaymentsPV += PaymentsPV[t]; 
	}
    return SumOfPaymentsPV
}










/// ################################
/// ################################


var R = 0.06 / 12; ///++R:++ Monthly **mortgage rate**.
var T = 30 * 12; ///++T:++ **How long** it takes **until you to pay off principal** you owe if you keep on making the **same monthly payments**? a.k.a., amortization period.


var AnnuityPayments   = AnnuityPayments(T); ///++AnnuityPayments:++ Sequence of **$1 payments** for each of the **next **_**T**_** months**.

var AnnuityPaymentsPV = PresentValue(AnnuityPayments,R); ///++AnnuityPaymentsPV:++ The **present value** of each of the **$1 annuity payments** from month t=1 to month t=T.










/// ################################
/// ################################

Sum(AnnuityPaymentsPV); ///**Sum** of the **present value** of **$1 annuity payments** over **next T months**.
var A = (1/R) * (1 - 1/((1+R)**T)); ///++A:++ **Present value** of a **T-month $1 annuity** if the **monthly interest rate is R** computed using the annuity formula. Better be **equal to sum of present value of annuity payments**!!!

monthlyPayment.js

var InitialBalance = 500; ///++InitialBalance:++ **Amount you borrow** from the bank (in $1000s).
var R              = 0.06 / 12; ///++R:++ Monthly **mortgage rate**.
var T              = 30 * 12; ///++T:++ **How long** it takes **until you to pay off principal** you owe if you keep on making the **same monthly payments**? a.k.a., amortization period.

/// ################################
/// ################################

var A = (1/R) * (1 - 1/((1+R)**T)); ///++A:++ **Present value** of a **T-month $1 annuity** if the **monthly interest rate is R**.

/// ################################
/// ################################

var MonthlyPayment    = InitialBalance / A; ///++MonthlyPayment:++ **Amount you pay** each month (in $1000s) for **next T months** if you **borrow InitialBalance** from the bank when the monthly **mortgage rate is R**.
var MonthlyPaymentsPV = MonthlyPayment * A; ///++MonthlyPaymentsPV:++ **Present value** of your **monthly payments** for the **next T months** if the **mortgage rate is R** (in $1000s). Better be **same as InitialBalance**, or else someone screwed up!!!